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Popular Calculus >

derivative of P(x)=x(x-8)(x+5)

Solution

derivative of

P (x) = x (x - 8) (x + 5)

Solution

3 x^{2} - 6 x - 40

Solution steps

\frac{d}{d x} (x (x - 8) (x + 5))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (x - 8) (x + 5)

= \frac{d x}{d x} (x - 8) (x + 5) + \frac{d}{d x} ((x - 8) (x + 5)) x

\frac{d x}{d x} = 1

\frac{d}{d x} ((x - 8) (x + 5)) = 2 x - 3

= 1 \cdot (x - 8) (x + 5) + (2 x - 3) x

Simplify

1 \cdot (x - 8) (x + 5) + (2 x - 3) x : 3 x^{2} - 6 x - 40

= 3 x^{2} - 6 x - 40

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of P(x)=x(x-8)(x+5) ?
The derivative of P(x)=x(x-8)(x+5) is 3x^2-6x-40
What is the first derivative of P(x)=x(x-8)(x+5) ?
The first derivative of P(x)=x(x-8)(x+5) is 3x^2-6x-40